Take Home Exercise 3

Author

Kieren Chua

Published

November 1, 2024

Modified

Invalid Date

Part 1 : Data And Packages

Packages

pacman::p_load(sf, spdep, GWmodel, SpatialML, 
               tmap, rsample, Metrics, tidyverse,
               knitr, kableExtra, jsonlite)

Data

We can get the lat long data from the previous output

location_data <- read_rds("data/processed_data/coords.rds")

resale_data <- read_csv("data/resale.csv")
Rows: 192970 Columns: 11
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (8): month, town, flat_type, block, street_name, storey_range, flat_mode...
dbl (3): floor_area_sqm, lease_commence_date, resale_price

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
resale_tidy <- resale_data %>%
  mutate(address = paste(block,street_name)) %>%
  mutate(remaining_lease_yr = as.integer(
    str_sub(remaining_lease, 0, 2)))%>%
  mutate(remaining_lease_mth = as.integer(
    str_sub(remaining_lease, 9, 11)))

We also got data from the other required decision parameters, which are :

Structural factors

  1. Area of the unit
  2. Floor level Remaining
  3. lease
  4. Age of the unit

Locational factors

  1. Proxomity to CBD
  2. Proximity to eldercare
  3. Proximity to foodcourt/hawker centres
  4. Proximity to MRT
  5. Proximity to park
  6. Proximity to good primary school ( All schools are good schools lol)
  7. Proximity to shopping mall
  8. Proximity to supermarket
  9. Numbers of kindergartens within 350m
  10. Numbers of childcare centres within 350m
  11. Numbers of bus stop within 350m
  12. Numbers of primary school within 1km
CBD_lat_long <- c(1.287953, 103.851784) # Taken from https://www.latlong.net/place/downtown-core-singapore-20616.html

CBD_svy21 <- st_sfc(st_point(c(103.851784, 1.287953)), 
                    crs = 4326) %>%
                    st_transform(3414)
eldercare_data <- st_read(dsn = "data/EldercareServicesSHP", 
                          layer = "ELDERCARE") %>% st_transform(3414)
Reading layer `ELDERCARE' from data source 
  `C:\Users\Admin\Desktop\SMU\ISSS626\ISSS626-KierenChua\TakeHomeEx\TakeHomeEx03\data\EldercareServicesSHP' 
  using driver `ESRI Shapefile'
Simple feature collection with 133 features and 18 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 14481.92 ymin: 28218.43 xmax: 41665.14 ymax: 46804.9
Projected CRS: SVY21
foodcourt_data <- st_read("data/HawkerCentresGEOJSON.geojson") %>% st_transform(3414)
Reading layer `HawkerCentresGEOJSON' from data source 
  `C:\Users\Admin\Desktop\SMU\ISSS626\ISSS626-KierenChua\TakeHomeEx\TakeHomeEx03\data\HawkerCentresGEOJSON.geojson' 
  using driver `GeoJSON'
Simple feature collection with 125 features and 2 fields
Geometry type: POINT
Dimension:     XYZ
Bounding box:  xmin: 103.6974 ymin: 1.272716 xmax: 103.9882 ymax: 1.449017
z_range:       zmin: 0 zmax: 0
Geodetic CRS:  WGS 84
MRT_data <- st_read("data/LTAMRTStationExitGEOJSON.geojson") %>% st_transform(3414)
Reading layer `LTAMRTStationExitGEOJSON' from data source 
  `C:\Users\Admin\Desktop\SMU\ISSS626\ISSS626-KierenChua\TakeHomeEx\TakeHomeEx03\data\LTAMRTStationExitGEOJSON.geojson' 
  using driver `GeoJSON'
Simple feature collection with 563 features and 2 fields
Geometry type: POINT
Dimension:     XYZ
Bounding box:  xmin: 103.6368 ymin: 1.264972 xmax: 103.9893 ymax: 1.449157
z_range:       zmin: 0 zmax: 0
Geodetic CRS:  WGS 84
park_data <- st_read("data/Parks.kml") %>% st_transform(3414)
Reading layer `NATIONALPARKS' from data source 
  `C:\Users\Admin\Desktop\SMU\ISSS626\ISSS626-KierenChua\TakeHomeEx\TakeHomeEx03\data\Parks.kml' 
  using driver `KML'
Simple feature collection with 430 features and 2 fields
Geometry type: POINT
Dimension:     XYZ
Bounding box:  xmin: 103.6929 ymin: 1.214491 xmax: 104.0538 ymax: 1.462094
z_range:       zmin: 0 zmax: 0
Geodetic CRS:  WGS 84
primarySchool_data <- st_read("data/LTASchoolZone.geojson") %>% st_transform(3414)
Reading layer `LTASchoolZone' from data source 
  `C:\Users\Admin\Desktop\SMU\ISSS626\ISSS626-KierenChua\TakeHomeEx\TakeHomeEx03\data\LTASchoolZone.geojson' 
  using driver `GeoJSON'
Simple feature collection with 211 features and 2 fields
Geometry type: MULTIPOLYGON
Dimension:     XY, XYZ
Bounding box:  xmin: 103.687 ymin: 1.272736 xmax: 103.9668 ymax: 1.457587
z_range:       zmin: 0 zmax: 0
Geodetic CRS:  WGS 84
Warning in CPL_transform(x, crs, aoi, pipeline, reverse, desired_accuracy, :
GDAL Message 1: Sub-geometry 0 has coordinate dimension 2, but container has 3
Warning in CPL_transform(x, crs, aoi, pipeline, reverse, desired_accuracy, :
GDAL Message 1: Sub-geometry 1 has coordinate dimension 2, but container has 3
mall_data <- st_read(dsn = "data/MP14SDCPPWPLANMallandPromenadeSHP", 
                     layer="G_MP14_PKWB_MALL_PROM_PL") %>% st_transform(3414)
Reading layer `G_MP14_PKWB_MALL_PROM_PL' from data source 
  `C:\Users\Admin\Desktop\SMU\ISSS626\ISSS626-KierenChua\TakeHomeEx\TakeHomeEx03\data\MP14SDCPPWPLANMallandPromenadeSHP' 
  using driver `ESRI Shapefile'
Simple feature collection with 464 features and 8 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 15576.2 ymin: 24936 xmax: 40537.72 ymax: 48239.39
Projected CRS: SVY21
supermarket_data <- st_read("data/SupermarketsGEOJSON.geojson") %>% st_transform(3414)
Reading layer `SupermarketsGEOJSON' from data source 
  `C:\Users\Admin\Desktop\SMU\ISSS626\ISSS626-KierenChua\TakeHomeEx\TakeHomeEx03\data\SupermarketsGEOJSON.geojson' 
  using driver `GeoJSON'
Simple feature collection with 526 features and 2 fields
Geometry type: POINT
Dimension:     XYZ
Bounding box:  xmin: 103.6258 ymin: 1.24715 xmax: 104.0036 ymax: 1.461526
z_range:       zmin: 0 zmax: 0
Geodetic CRS:  WGS 84
kindergarten_data <- st_read("data/Kindergartens.geojson") %>% st_transform(3414)
Reading layer `Kindergartens' from data source 
  `C:\Users\Admin\Desktop\SMU\ISSS626\ISSS626-KierenChua\TakeHomeEx\TakeHomeEx03\data\Kindergartens.geojson' 
  using driver `GeoJSON'
Simple feature collection with 448 features and 2 fields
Geometry type: POINT
Dimension:     XYZ
Bounding box:  xmin: 103.6887 ymin: 1.247759 xmax: 103.9717 ymax: 1.455452
z_range:       zmin: 0 zmax: 0
Geodetic CRS:  WGS 84
childcare_data <- st_read("data/ChildCareServices.geojson") %>% st_transform(3414)
Reading layer `ChildCareServices' from data source 
  `C:\Users\Admin\Desktop\SMU\ISSS626\ISSS626-KierenChua\TakeHomeEx\TakeHomeEx03\data\ChildCareServices.geojson' 
  using driver `GeoJSON'
Simple feature collection with 1925 features and 2 fields
Geometry type: POINT
Dimension:     XYZ
Bounding box:  xmin: 103.6878 ymin: 1.247759 xmax: 103.9897 ymax: 1.462134
z_range:       zmin: 0 zmax: 0
Geodetic CRS:  WGS 84
busstop_data <- st_read(dsn = "data/BusStopLocation_Jul2024",
                        layer= "BusStop") %>% st_transform(3414)
Reading layer `BusStop' from data source 
  `C:\Users\Admin\Desktop\SMU\ISSS626\ISSS626-KierenChua\TakeHomeEx\TakeHomeEx03\data\BusStopLocation_Jul2024' 
  using driver `ESRI Shapefile'
Simple feature collection with 5166 features and 3 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 3970.122 ymin: 26482.1 xmax: 48285.52 ymax: 52983.82
Projected CRS: SVY21

Part 2 : Processing the data

Now we need to add all the data to the dataframe

Locations of HDB

We can use the location data and join by postal code

resale_tidy_loc <- left_join(resale_tidy, location_data, by = "address")
resale_tidy_clean <- resale_tidy_loc %>% 
                filter(!is.na(postal))

# Then we convert the lat long into SVY21
resale_sf <- st_as_sf(resale_tidy_clean, 
                      coords = c("longitude", "latitude"),
                      crs = 4326) %>%
            st_transform(3414)

# Handle the NA in the lease months
resale_sf$remaining_lease_mth[is.na(resale_sf$remaining_lease_mth)] <- 0

We also need to jitter the points so that the points do not share the same coordinates, we need to jitter quite abit for the regression to work latter.

resale_sf$geometry <- st_jitter(resale_sf$geometry, amount = 100)

We can now show the data

tmap_mode("plot")
tmap mode set to plotting
tm_shape(resale_sf) + 
  tm_dots()

Unit Age

resale_sf$unit_age <- 99 - resale_sf$remaining_lease_yr

Proximity to CBD

We can compare all locations to the single CBD coordinate and output a distance

distance_matrix <- st_distance(resale_sf$geometry, CBD_svy21)

resale_sf$PROX_CBD <- apply(distance_matrix, 1, min)

Proximity to Eldercare

In this case we can find the closest elder-care to the HDB unit

distance_matrix <- st_distance(resale_sf$geometry, eldercare_data$geometry)

resale_sf$PROX_ELDER <- apply(distance_matrix, 1, min)

Proximity to Hawker Center

We do the same thing here

distance_matrix <- st_distance(resale_sf$geometry, foodcourt_data$geometry)

resale_sf$PROX_HAWKER <- apply(distance_matrix, 1, min)

Proximity to MRT

distance_matrix <- st_distance(resale_sf$geometry, MRT_data$geometry)

resale_sf$PROX_MRT <- apply(distance_matrix, 1, min)

Proximity to Park

distance_matrix <- st_distance(resale_sf$geometry, park_data$geometry)

resale_sf$PROX_PARK <- apply(distance_matrix, 1, min)

Proximity to Primary School

We need to get the center of the primary school to compare against centroid. Need to drop the z value

primarySchool_data$geometry <- st_zm(primarySchool_data$geometry)
primarySchool_data$centroid <- st_centroid(primarySchool_data$geometry)
distance_matrix <- st_distance(resale_sf$geometry, primarySchool_data$centroid)

resale_sf$PROX_PRIM <- apply(distance_matrix, 1, min)

Proximity to Shopping Mall

Same for the shopping mall

mall_data$centroid <- st_centroid(mall_data$geometry)
distance_matrix <- st_distance(resale_sf$geometry, mall_data$centroid)

resale_sf$PROX_MALL <- apply(distance_matrix, 1, min)

Proximity to Supermarket

distance_matrix <- st_distance(resale_sf$geometry, supermarket_data$geometry)

resale_sf$PROX_SPMK <- apply(distance_matrix, 1, min)

Number of Kindergartens within 350m

To calculate the number of kindergartens within 350m of the HBD, we need to have a 350m search radius around each location, then count the number of kindergartens within

distance_matrix <- st_distance(resale_sf$geometry, kindergarten_data$geometry)

count_within_350m <- apply(distance_matrix, 1, function(distances) {
  sum(distances <= 350)  # Count points within 350 meters
})

resale_sf$KIND_350 <- count_within_350m

Number of Childcares within 350m

distance_matrix <- st_distance(resale_sf$geometry, st_zm(childcare_data$geometry))

count_within_350m <- apply(distance_matrix, 1, function(distances) {
  sum(distances <= 350)  # Count points within 350 meters
})

resale_sf$CHILD_350 <- count_within_350m

Number of Bus-Stops within 350m

distance_matrix <- st_distance(resale_sf$geometry, busstop_data$geometry)

count_within_350m <- apply(distance_matrix, 1, function(distances) {
  sum(distances <= 350)  # Count points within 350 meters
})

resale_sf$BUS_350 <- count_within_350m

Number of Primary School within 1000m

distance_matrix <- st_distance(resale_sf$geometry, primarySchool_data$centroid)

count_within_1km <- apply(distance_matrix, 1, function(distances) {
  sum(distances <= 1000)  # Count points within 350 meters
})

resale_sf$PRI_1K <- count_within_1km

Saving the data

Now we can save the data for future purposes.

write_rds(resale_sf, "data/resale_sf_processed.rds")

Part 3 : Shrinking the search space

Read the data

cleaned_resale_sf <- read_rds("data/resale_sf_processed.rds")
cleaned_resale_no_geom <- cleaned_resale_sf %>% st_drop_geometry()

Because there is too much data, we will need to reduce the size of inspection. First we shall determine the types of flats available.

unique_flat_types <- unique(cleaned_resale_sf$flat_type)
unique_flat_types
[1] "3 ROOM"    "4 ROOM"    "5 ROOM"    "EXECUTIVE" "2 ROOM"

We also want to see the types of flats that are available

unique_flat_models <- unique(cleaned_resale_sf$flat_model)
unique_flat_models
 [1] "New Generation"         "DBSS"                   "Improved"              
 [4] "Apartment"              "Simplified"             "Model A"               
 [7] "Model A-Maisonette"     "Maisonette"             "Standard"              
[10] "Premium Apartment"      "Type S1"                "Model A2"              
[13] "Type S2"                "Adjoined flat"          "Premium Apartment Loft"
[16] "2-room"                 "Premium Maisonette"     "3Gen"

To have more focus on the data, we shall focus on the more expensive apartments vs the exercise given to us. To get an idea of what is expensive, we will need to see the spread of flat prices

boxplot(cleaned_resale_sf$resale_price, main="Box plot of resale prices", ylab="Resale Price")

We can see there are many outliers of data from the boxplot in the upper half. To maintain a large amount of data, we shall use the top 25% of data as the search space

sale_quantiles <- quantile(cleaned_resale_sf$resale_price)

sale_quantiles[4]
   75% 
629000

So the upper quantile is 629 000 dollars, we shall round that down to 600 000 and then only consider rooms above that price.

cleaned_resale_sf_cut <- cleaned_resale_sf %>% 
                          filter(resale_price >= 6e5)
cleaned_resale_sf_cut_no_geom <- cleaned_resale_sf_cut %>%
                                  st_drop_geometry()

This leaves us with over 10000 data samples, which should be enough for us.

Part 4 : Computing Correlation Matrix

Bin the data

We need to bin some of the variables so that they make integers

Storeys

unqiue_storey <- unique(cleaned_resale_sf_cut_no_geom$storey_range)

storey_mapping <- setNames(seq_along(unqiue_storey), unqiue_storey)

cleaned_resale_sf_cut_no_geom$storey_range_bin <- storey_mapping[cleaned_resale_sf_cut_no_geom$storey_range]
cleaned_resale_sf_cut$storey_range_bin <- storey_mapping[cleaned_resale_sf_cut$storey_range]

Plotting the graph

We are not sure if all the variables are correlated, so we can build a correlation matrix to see if we need to exclude any variables

required_cols <- c(7, 9, 13, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29)
corrplot::corrplot(cor(cleaned_resale_sf_cut_no_geom[, required_cols]), 
                   diag = FALSE, 
                   order = "AOE",
                   tl.pos = "td", 
                   tl.cex = 0.5, 
                   method = "number", 
                   type = "upper")

We can see that lease commence date and lease remaining year has a correlation value of more than 0.8, so we can remove them from the choices

Variance Inflation Factor

We also can check the Variance Inflation Factor to see if there are any variables above a 5

Train-Test Split

First we need to do a train test split for any model training. Split shall be 65 - 35.

set.seed(1234)
# First we try to remove any NA values
cleaned_resale_sf_cut <- cleaned_resale_sf_cut[rowSums(is.na(st_drop_geometry(cleaned_resale_sf_cut))) == 0,, ]

resale_split <- initial_split(cleaned_resale_sf_cut, 
                              prop = 6.5/10,)
# We use a 80/20 split since we have more than 40000 samples of data
train_data <- training(resale_split)

Generating simple LM Model

price_mlr <- lm(resale_price ~ floor_area_sqm + storey_range_bin + remaining_lease_yr +
                  PROX_CBD + PROX_ELDER + PROX_HAWKER +
                  PROX_MRT + PROX_PARK + PROX_MALL +
                  PROX_SPMK + KIND_350 +
                  CHILD_350 + BUS_350 +
                  PRI_1K,
                data=train_data)
vif <- performance::check_collinearity(price_mlr)
kable(vif, 
      caption = "Variance Inflation Factor (VIF) Results") %>%
  kable_styling(font_size = 18)
Variance Inflation Factor (VIF) Results
Term VIF VIF_CI_low VIF_CI_high SE_factor Tolerance Tolerance_CI_low Tolerance_CI_high
floor_area_sqm 2.123886 2.060393 2.191180 1.457356 0.4708351 0.4563750 0.4853442
storey_range_bin 1.036499 1.020201 1.065949 1.018086 0.9647858 0.9381311 0.9801993
remaining_lease_yr 1.871208 1.817733 1.928181 1.367921 0.5344141 0.5186236 0.5501359
PROX_CBD 2.378824 2.305242 2.456553 1.542344 0.4203759 0.4070745 0.4337938
PROX_ELDER 1.373721 1.340160 1.410593 1.172058 0.7279500 0.7089217 0.7461797
PROX_HAWKER 1.455691 1.418806 1.495825 1.206520 0.6869590 0.6685275 0.7048181
PROX_MRT 1.107995 1.086099 1.135459 1.052614 0.9025310 0.8807009 0.9207261
PROX_PARK 1.253436 1.224856 1.285648 1.119570 0.7978070 0.7778177 0.8164223
PROX_MALL 1.370811 1.337369 1.407568 1.170816 0.7294952 0.7104452 0.7477370
PROX_SPMK 1.116288 1.093951 1.143935 1.056545 0.8958264 0.8741753 0.9141179
KIND_350 1.416146 1.380860 1.454700 1.190019 0.7061421 0.6874267 0.7241866
CHILD_350 1.493679 1.455264 1.535336 1.222162 0.6694878 0.6513231 0.6871608
BUS_350 1.165329 1.140608 1.194397 1.079504 0.8581267 0.8372425 0.8767257
PRI_1K 1.392592 1.358262 1.430211 1.180081 0.7180855 0.6991976 0.7362349

We can also plot this out for better visualization

plot(vif) +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))
Variable `Component` is not in your data frame :/

We can see that all the variables have a variables that is below a 5, so we can use all of them.

Part 5 : Generating Geographically Weighted Predictive Models

Convert to Spatial Datframe

# First we check for NA values in the traindata

train_data_sp <- as_Spatial(train_data)

Get adaptive bandwidth

bw_adaptive <- bw.gwr(resale_price ~ floor_area_sqm +
                  storey_range_bin + remaining_lease_yr +
                  PROX_CBD + PROX_ELDER + PROX_HAWKER +
                  PROX_MRT + PROX_PARK + PROX_MALL + 
                  PROX_SPMK + KIND_350 +
                  CHILD_350 + BUS_350 +
                  PRI_1K,
                  data=train_data_sp,
                  approach="CV",
                  kernel="gaussian",
                  adaptive=TRUE,
                  longlat=FALSE)
Take a cup of tea and have a break, it will take a few minutes.
          -----A kind suggestion from GWmodel development group
Adaptive bandwidth: 5848 CV score: 9.243392e+13 
Adaptive bandwidth: 3622 CV score: 9.014497e+13 
Adaptive bandwidth: 2245 CV score: 8.697263e+13 
Adaptive bandwidth: 1395 CV score: 8.349133e+13 
Adaptive bandwidth: 869 CV score: 7.899485e+13 
Adaptive bandwidth: 544 CV score: 7.466116e+13 
Adaptive bandwidth: 343 CV score: 7.086881e+13 
Adaptive bandwidth: 219 CV score: 6.661355e+13 
Adaptive bandwidth: 142 CV score: 6.541905e+13 
Adaptive bandwidth: 94 CV score: 6.76693e+13 
Adaptive bandwidth: 171 CV score: 6.621383e+13 
Adaptive bandwidth: 123 CV score: 6.475166e+13 
Adaptive bandwidth: 112 CV score: 6.437627e+13 
Adaptive bandwidth: 104 CV score: 6.420869e+13 
Adaptive bandwidth: 100 CV score: 6.410668e+13 
Adaptive bandwidth: 97 CV score: 6.406601e+13 
Adaptive bandwidth: 95 CV score: 3.245186e+32 
Adaptive bandwidth: 98 CV score: 6.407292e+13 
Adaptive bandwidth: 96 CV score: 6.400365e+13 
Adaptive bandwidth: 95 CV score: 3.245186e+32 
Adaptive bandwidth: 96 CV score: 6.400365e+13

We will also save it for the future

write_rds(bw_adaptive, "data/model/bw_adaptive.rds")
bw_adaptive <- read_rds("data/model/bw_adaptive.rds")

Make the model

Now we will make the adaptive GWR model

gwr_adaptive <- gwr.basic(formula = resale_price ~ floor_area_sqm +
                  storey_range_bin + remaining_lease_yr +
                  PROX_CBD + PROX_ELDER + PROX_HAWKER +
                  PROX_MRT + PROX_PARK + PROX_MALL + 
                  PROX_SPMK + KIND_350 +
                  CHILD_350 + BUS_350 +
                  PRI_1K,
                          data=train_data_sp,
                          bw=bw_adaptive, 
                          kernel = 'gaussian', 
                          adaptive=TRUE,
                          longlat = FALSE)

Save a copy

write_rds(gwr_adaptive, "data/model/gwr_adaptive.rds")

Reading the model

gwr_adaptive <- read_rds("data/model/gwr_adaptive.rds")
gwr_adaptive
   ***********************************************************************
   *                       Package   GWmodel                             *
   ***********************************************************************
   Program starts at: 2024-11-04 10:54:08.130745 
   Call:
   gwr.basic(formula = resale_price ~ floor_area_sqm + storey_range_bin + 
    remaining_lease_yr + PROX_CBD + PROX_ELDER + PROX_HAWKER + 
    PROX_MRT + PROX_PARK + PROX_MALL + PROX_SPMK + KIND_350 + 
    CHILD_350 + BUS_350 + PRI_1K, data = train_data_sp, bw = bw_adaptive, 
    kernel = "gaussian", adaptive = TRUE, longlat = FALSE)

   Dependent (y) variable:  resale_price
   Independent variables:  floor_area_sqm storey_range_bin remaining_lease_yr PROX_CBD PROX_ELDER PROX_HAWKER PROX_MRT PROX_PARK PROX_MALL PROX_SPMK KIND_350 CHILD_350 BUS_350 PRI_1K
   Number of data points: 9451
   ***********************************************************************
   *                    Results of Global Regression                     *
   ***********************************************************************

   Call:
    lm(formula = formula, data = data)

   Residuals:
    Min      1Q  Median      3Q     Max 
-300000  -66120   -8029   54789  600034 

   Coefficients:
                        Estimate Std. Error t value Pr(>|t|)    
   (Intercept)         1.118e+05  1.604e+04   6.971 3.37e-12 ***
   floor_area_sqm      4.071e+03  7.401e+01  55.011  < 2e-16 ***
   storey_range_bin    3.689e+03  3.407e+02  10.826  < 2e-16 ***
   remaining_lease_yr  4.602e+03  1.217e+02  37.803  < 2e-16 ***
   PROX_CBD           -1.650e+01  3.508e-01 -47.031  < 2e-16 ***
   PROX_ELDER          9.124e-01  2.428e+00   0.376  0.70705    
   PROX_HAWKER        -2.515e+01  2.766e+00  -9.092  < 2e-16 ***
   PROX_MRT           -3.251e+01  3.103e+00 -10.474  < 2e-16 ***
   PROX_PARK          -1.287e+01  2.784e+00  -4.622 3.84e-06 ***
   PROX_MALL          -1.325e+01  1.038e+00 -12.766  < 2e-16 ***
   PROX_SPMK           3.758e+01  7.310e+00   5.142 2.78e-07 ***
   KIND_350            1.492e+02  1.115e+03   0.134  0.89358    
   CHILD_350           1.506e+03  5.591e+02   2.693  0.00709 ** 
   BUS_350             2.600e+03  3.957e+02   6.571 5.25e-11 ***
   PRI_1K             -4.598e+03  7.453e+02  -6.169 7.15e-10 ***

   ---Significance stars
   Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
   Residual standard error: 100400 on 9436 degrees of freedom
   Multiple R-squared: 0.4302
   Adjusted R-squared: 0.4293 
   F-statistic: 508.8 on 14 and 9436 DF,  p-value: < 2.2e-16 
   ***Extra Diagnostic information
   Residual sum of squares: 9.517932e+13
   Sigma(hat): 100364.1
   AIC:  244536.8
   AICc:  244536.8
   BIC:  235346.7
   ***********************************************************************
   *          Results of Geographically Weighted Regression              *
   ***********************************************************************

   *********************Model calibration information*********************
   Kernel function: gaussian 
   Adaptive bandwidth: 96 (number of nearest neighbours)
   Regression points: the same locations as observations are used.
   Distance metric: Euclidean distance metric is used.

   ****************Summary of GWR coefficient estimates:******************
                             Min.     1st Qu.      Median     3rd Qu.
   Intercept          -2.2161e+08 -3.9447e+05  2.3362e+05  1.0175e+06
   floor_area_sqm      5.7881e+02  3.0150e+03  4.4597e+03  6.4886e+03
   storey_range_bin   -1.0897e+04 -2.2363e+03 -4.0654e+02  2.3511e+03
   remaining_lease_yr -4.5221e+04 -3.7742e+03  1.3836e+03  4.3692e+03
   PROX_CBD           -4.3089e+03 -5.8548e+01 -8.2466e+00  5.2746e+01
   PROX_ELDER         -1.2694e+04 -3.8395e+01  9.2124e+00  7.7290e+01
   PROX_HAWKER        -2.8057e+04 -9.5238e+01 -1.2423e+01  5.8582e+01
   PROX_MRT           -5.3975e+03 -7.1185e+01 -9.9480e+00  7.0932e+01
   PROX_PARK          -6.4208e+03 -1.4255e+02 -2.8937e+01  3.0632e+01
   PROX_MALL          -3.6982e+04 -1.4251e+02 -1.8509e+01  3.2341e+01
   PROX_SPMK          -1.6215e+03 -6.1334e+01  6.4511e+00  1.1628e+02
   KIND_350           -3.7195e+05 -9.7700e+03 -2.6817e+03  8.0525e+03
   CHILD_350          -4.3973e+04 -4.7274e+03  1.0222e+03  6.4265e+03
   BUS_350            -2.6895e+04 -2.0684e+03  5.2201e+02  2.7924e+03
   PRI_1K             -8.5880e+05 -8.6240e+03  1.9411e+03  1.2431e+04
                            Max.
   Intercept          39372792.4
   floor_area_sqm        10209.9
   storey_range_bin      14261.9
   remaining_lease_yr    11105.9
   PROX_CBD              32763.3
   PROX_ELDER             2546.9
   PROX_HAWKER           14993.8
   PROX_MRT               8302.1
   PROX_PARK              7010.7
   PROX_MALL              5511.8
   PROX_SPMK             36702.7
   KIND_350             343934.6
   CHILD_350             38966.2
   BUS_350               23048.4
   PRI_1K               291799.6
   ************************Diagnostic information*************************
   Number of data points: 9451 
   Effective number of parameters (2trace(S) - trace(S'S)): 858.937 
   Effective degrees of freedom (n-2trace(S) + trace(S'S)): 8592.063 
   AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 240309.3 
   AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 239515.2 
   BIC (GWR book, Fotheringham, et al. 2002,GWR p. 61, eq. 2.34): 235646.4 
   Residual sum of squares: 5.221577e+13 
   R-square value:  0.6873985 
   Adjusted R-square value:  0.6561445 

   ***********************************************************************
   Program stops at: 2024-11-04 10:55:12.949854

From the results we can see that proximity to elder-care, number of child-cares and number of kindergartens seem to be insignificant to the resale price of the location. This could probably signify that these metrics may not be in consideration when people are making a purchase. We can try to remove its from future training.

Computer Test Data Adaptive Bandwidth

test_data <- testing(resale_split)
test_data_sp <- as_Spatial(test_data)
gwr_bw_test_adaptive <- bw.gwr(resale_price ~ floor_area_sqm +
                  storey_range_bin + remaining_lease_yr +
                  PROX_CBD + PROX_ELDER + PROX_HAWKER +
                  PROX_MRT + PROX_PARK + PROX_MALL + 
                  PROX_SPMK + KIND_350 +
                  CHILD_350 + BUS_350 +
                  PRI_1K,
                  data=test_data_sp,
                  approach="CV",
                  kernel="gaussian",
                  adaptive=TRUE,
                  longlat=FALSE)
Take a cup of tea and have a break, it will take a few minutes.
          -----A kind suggestion from GWmodel development group
Adaptive bandwidth: 3152 CV score: 5.095984e+13 
Adaptive bandwidth: 1956 CV score: 4.955062e+13 
Adaptive bandwidth: 1215 CV score: 4.78703e+13 
Adaptive bandwidth: 759 CV score: 4.59419e+13 
Adaptive bandwidth: 475 CV score: 4.374012e+13 
Adaptive bandwidth: 301 CV score: 4.162405e+13 
Adaptive bandwidth: 192 CV score: 3.970175e+13 
Adaptive bandwidth: 126 CV score: 3.789844e+13 
Adaptive bandwidth: 84 CV score: 3.633732e+13 
Adaptive bandwidth: 59 CV score: 3.538126e+13 
Adaptive bandwidth: 42 CV score: 3.505121e+13 
Adaptive bandwidth: 33 CV score: 3.489163e+13 
Adaptive bandwidth: 26 CV score: Inf 
Adaptive bandwidth: 36 CV score: 3.48701e+13 
Adaptive bandwidth: 39 CV score: 3.498059e+13 
Adaptive bandwidth: 35 CV score: 3.486166e+13 
Adaptive bandwidth: 33 CV score: 3.489163e+13 
Adaptive bandwidth: 34 CV score: 3.492213e+13 
Adaptive bandwidth: 33 CV score: 3.489163e+13 
Adaptive bandwidth: 34 CV score: 3.492213e+13 
Adaptive bandwidth: 33 CV score: 3.489163e+13 
Adaptive bandwidth: 33 CV score: 3.489163e+13 
Adaptive bandwidth: 32 CV score: 3.496297e+13 
Adaptive bandwidth: 32 CV score: 3.496297e+13 
Adaptive bandwidth: 31 CV score: 3.513044e+13 
Adaptive bandwidth: 31 CV score: 3.513044e+13 
Adaptive bandwidth: 30 CV score: 3.815501e+13 
Adaptive bandwidth: 30 CV score: 3.815501e+13 
Adaptive bandwidth: 29 CV score: 3.598842e+13 
Adaptive bandwidth: 29 CV score: 3.598842e+13 
Adaptive bandwidth: 28 CV score: Inf 
Adaptive bandwidth: 28 CV score: Inf 
Adaptive bandwidth: 27 CV score: 2.995955e+36 
Adaptive bandwidth: 27 CV score: 2.995955e+36 
Adaptive bandwidth: 26 CV score: Inf 
Adaptive bandwidth: 26 CV score: Inf 
Adaptive bandwidth: 25 CV score: Inf 
Adaptive bandwidth: 25 CV score: Inf

Now we can run prediction on the test dataset

Running Predictions on the test data

st_crs(train_data_sp)
Coordinate Reference System:
  User input: SVY21 / Singapore TM 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]
#gwr_pred <- gwr.predict(formula = resale_price ~ floor_area_sqm +
#                  storey_range_bin + remaining_lease_yr +
#                  PROX_CBD + PROX_ELDER + PROX_HAWKER +
#                  PROX_MRT + PROX_PARK + PROX_MALL + 
#                  PROX_SPMK + KIND_350 +
#                  CHILD_350 + BUS_350 +
#                  PRI_1K, 
#                  data= train_data_sp, 
#                  predictdata = test_data_sp, 
#                  bw=bw_adaptive, 
#                  kernel = 'gaussian', 
#                  adaptive= TRUE, 
#                  longlat = FALSE)

Part 7 : Generating Random Forest Model

Now we can move on to creating the random forest model

coords_train <- st_coordinates(train_data)
coords_test <- st_coordinates(test_data)
train_data_nogeom <- train_data %>%
  st_drop_geometry()

After preparing the data, we can train the model below

Basic Random Forest

set.seed(1234)
rf <- ranger(resale_price ~ floor_area_sqm +
                  storey_range_bin + remaining_lease_yr +
                  PROX_CBD + PROX_ELDER + PROX_HAWKER +
                  PROX_MRT + PROX_PARK + PROX_MALL + 
                  PROX_SPMK + KIND_350 +
                  CHILD_350 + BUS_350 +
                  PRI_1K,
             data=train_data_nogeom)

We can view the model output below

rf
Ranger result

Call:
 ranger(resale_price ~ floor_area_sqm + storey_range_bin + remaining_lease_yr +      PROX_CBD + PROX_ELDER + PROX_HAWKER + PROX_MRT + PROX_PARK +      PROX_MALL + PROX_SPMK + KIND_350 + CHILD_350 + BUS_350 +      PRI_1K, data = train_data_nogeom) 

Type:                             Regression 
Number of trees:                  500 
Sample size:                      9451 
Number of independent variables:  14 
Mtry:                             3 
Target node size:                 5 
Variable importance mode:         none 
Splitrule:                        variance 
OOB prediction error (MSE):       5023645049 
R squared (OOB):                  0.7157895

Cleaning up the data

The code now is taking up alot of space, so we nedd to clean up some of the data that we dont need for future

rm(rf)
rm(price_mlr)
rm(resale_split)
rm(gwr_adaptive)
rm(busstop_data)
rm(childcare_data)
rm(cleaned_resale_no_geom)
rm(cleaned_resale_sf)
rm(eldercare_data)
rm(foodcourt_data)
rm(kindergarten_data)
rm(mall_data)
rm(MRT_data)
rm(primarySchool_data)

Geographically weighted Random Forest

set.seed(1234)
gwRF_adaptive <- grf(formula = resale_price ~ floor_area_sqm +
                  storey_range_bin + remaining_lease_yr +
                  PROX_CBD + PROX_ELDER + PROX_HAWKER +
                  PROX_MRT + PROX_PARK + PROX_MALL + 
                  PROX_SPMK + KIND_350 +
                  CHILD_350 + BUS_350 +
                  PRI_1K,
                     dframe=train_data_nogeom, 
                     bw=bw_adaptive,
                     kernel="adaptive",
                     coords=coords_train)

Number of Observations: 9451
Number of Independent Variables: 14
Kernel: Adaptive
Neightbours: 96

--------------- Global ML Model Summary ---------------
Ranger result

Call:
 ranger(resale_price ~ floor_area_sqm + storey_range_bin + remaining_lease_yr +      PROX_CBD + PROX_ELDER + PROX_HAWKER + PROX_MRT + PROX_PARK +      PROX_MALL + PROX_SPMK + KIND_350 + CHILD_350 + BUS_350 +      PRI_1K, data = train_data_nogeom, num.trees = 500, mtry = 4,      importance = "impurity", num.threads = NULL) 

Type:                             Regression 
Number of trees:                  500 
Sample size:                      9451 
Number of independent variables:  14 
Mtry:                             4 
Target node size:                 5 
Variable importance mode:         impurity 
Splitrule:                        variance 
OOB prediction error (MSE):       4612949806 
R squared (OOB):                  0.7390244 

Importance:
    floor_area_sqm   storey_range_bin remaining_lease_yr           PROX_CBD 
      2.977832e+13       1.195320e+13       1.593509e+13       3.526793e+13 
        PROX_ELDER        PROX_HAWKER           PROX_MRT          PROX_PARK 
      7.796038e+12       9.779579e+12       8.871637e+12       8.831199e+12 
         PROX_MALL          PROX_SPMK           KIND_350          CHILD_350 
      1.344756e+13       6.735692e+12       1.891701e+12       3.445535e+12 
           BUS_350             PRI_1K 
      3.599768e+12       4.718909e+12 

Mean Square Error (Not OOB): 909027101.367
R-squared (Not OOB) %: 94.857
AIC (Not OOB): 194984.146
AICc (Not OOB): 194984.196

--------------- Local Model Summary ---------------

Residuals OOB:
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
-665000.0  -43548.6   -5918.9    -596.7   36662.9  432645.5 

Residuals Predicted (Not OOB):
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
-122863.1   -5467.1    -499.7     128.3    4456.8  164455.1 

Local Variable Importance:
                          Min          Max         Mean          StD
floor_area_sqm     1777954668 2.643120e+12 249085148532 286894587946
storey_range_bin   1321337404 5.600684e+11  61059195013  73326417657
remaining_lease_yr  633108120 1.027629e+12 138330018917 136874478584
PROX_CBD           4317027703 7.754116e+11  67033814042  58945224069
PROX_ELDER         3670833577 4.819070e+11  63884116919  47372929863
PROX_HAWKER        4351101712 1.134055e+12  66358702105  72657028429
PROX_MRT           4066713291 5.941267e+11  68159755980  63690255509
PROX_PARK          4416339936 8.330187e+11  64655468635  56254087077
PROX_MALL          4132483593 5.948118e+11  63897456639  54633020764
PROX_SPMK          4954693397 6.562553e+11  64878360646  56103764598
KIND_350                    0 9.685132e+10   5981484288   8332343133
CHILD_350                   0 1.973514e+11  18822223674  17860270451
BUS_350            2018011859 2.991237e+11  26645196055  24357940617
PRI_1K                      0 1.792149e+11   7900229926  11992377320

Mean squared error (OOB): 5827964401.412
R-squared (OOB) %: 67.025
AIC (OOB): 212544.559
AICc (OOB): 212544.609
Mean squared error Predicted (Not OOB): 164582017.25
R-squared Predicted (Not OOB) %: 99.069
AIC Predicted (Not OOB): 178832.709
AICc Predicted (Not OOB): 178832.76

Calculation time (in seconds): 39.8701

We can then save the model for future use

write_rds(gwRF_adaptive, "data/model/gwRF_adaptive.rds")

We then re-read it, mostly for running purposes

gwRF_adaptive <- read_rds("data/model/gwRF_adaptive.rds")

Predicting with test data

test_data_nogeom <- cbind(
  test_data, coords_test) %>%
  st_drop_geometry()
gwRF_pred <- predict.grf(gwRF_adaptive, 
                           test_data_nogeom, 
                           x.var.name="X",
                           y.var.name="Y", 
                           local.w=1,
                           global.w=0)
GRF_pred_df <- as.data.frame(gwRF_pred)

test_data_pred <- cbind(test_data,
                        GRF_pred_df)

Save the data for the future

write_rds(test_data_pred, "data/test_results.rds")
test_data_pred <- read_rds( "data/test_results.rds")

Freeing Memory

The model is very large >15Gb so once we got th results, we should free up the memory

rm(gwRF_adaptive)

Viewing Random Forest Prediction Error

Now we can compare the diffrence in values from predictions vs actual resale value by locaiton

rmse(test_data_pred$resale_price, 
     test_data_pred$gwRF_pred)
[1] 73299.75
ggplot(data = test_data_pred,
       aes(x = gwRF_pred,
           y = resale_price)) +
  geom_point()

We can see that there is a bottom out on the predictions, which is due to us cutting off the resale price limit at 600,000.

Show residuals

test_data_pred$residuals <- test_data_pred$gwRF_pred - test_data_pred$resale_price
st_crs(test_data_pred)
Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]
# Load in the mpsz data
mpsz = st_read(dsn = "data/geospatial", layer = "MP14_SUBZONE_WEB_PL") %>% st_transform(3414)
Reading layer `MP14_SUBZONE_WEB_PL' from data source 
  `C:\Users\Admin\Desktop\SMU\ISSS626\ISSS626-KierenChua\TakeHomeEx\TakeHomeEx03\data\geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 323 features and 15 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21

Plot the map

tmap_mode("view")
tmap mode set to interactive viewing
tm_shape(mpsz) +
    tmap_options(check.and.fix = TRUE) +
    tm_polygons(alpha = 0.4) +
tm_shape(test_data_pred) +
    tm_dots(col = "residuals",
            alpha = 0.6,
            style = "quantile")
Warning: The shape mpsz is invalid (after reprojection). See sf::st_is_valid
Variable(s) "residuals" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
tmap_mode("plot")
tmap mode set to plotting